IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v200y2010i3p658-670.html
   My bibliography  Save this article

A linear programming-based optimization algorithm for solving nonlinear programming problems

Author

Listed:
  • Still, Claus
  • Westerlund, Tapio

Abstract

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.

Suggested Citation

  • Still, Claus & Westerlund, Tapio, 2010. "A linear programming-based optimization algorithm for solving nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 658-670, February.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:658-670
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00046-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Still, Claus & Westerlund, Tapio, 2006. "A sequential cutting plane algorithm for solving convex NLP problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 444-464, September.
    2. R. E. Griffith & R. A. Stewart, 1961. "A Nonlinear Programming Technique for the Optimization of Continuous Processing Systems," Management Science, INFORMS, vol. 7(4), pages 379-392, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Trindade, Graça & Ambrósio, Jorge, 2012. "An optimization method to estimate models with store-level data: A case study," European Journal of Operational Research, Elsevier, vol. 217(3), pages 664-672.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammed Alfaki & Dag Haugland, 2013. "Strong formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 897-916, July.
    2. Sarker, Ruhul A. & Gunn, Eldon A., 1997. "A simple SLP algorithm for solving a class of nonlinear programs," European Journal of Operational Research, Elsevier, vol. 101(1), pages 140-154, August.
    3. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.
    4. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    5. Hagspiel, Simeon & Jägemann, Cosima & Lindenberger, Dietmar & Brown, Tom & Cherevatskiy, Stanislav & Tröster, Eckehard, 2013. "Cost-Optimal Power System Extension under Flow-Based Market Coupling," EWI Working Papers 2013-9, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI).
    6. Chen, Ruoran & Deng, Tianhu & Huang, Simin & Qin, Ruwen, 2015. "Optimal crude oil procurement under fluctuating price in an oil refinery," European Journal of Operational Research, Elsevier, vol. 245(2), pages 438-445.
    7. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
    8. B Felderer, 1975. "Optimal Allocation of Resources to the Educational Sector in a System of Regions," Environment and Planning A, , vol. 7(1), pages 59-70, February.
    9. Mohammed Alfaki & Dag Haugland, 2014. "A cost minimization heuristic for the pooling problem," Annals of Operations Research, Springer, vol. 222(1), pages 73-87, November.
    10. Johannes O. Royset & Hiroyuki Sato, 2010. "Route optimization for multiple searchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 701-717, December.
    11. Oldewurtel, Frauke & Sturzenegger, David & Morari, Manfred, 2013. "Importance of occupancy information for building climate control," Applied Energy, Elsevier, vol. 101(C), pages 521-532.
    12. Hagspiel, S. & Jägemann, C. & Lindenberger, D. & Brown, T. & Cherevatskiy, S. & Tröster, E., 2014. "Cost-optimal power system extension under flow-based market coupling," Energy, Elsevier, vol. 66(C), pages 654-666.
    13. Charles Audet & Jack Brimberg & Pierre Hansen & Sébastien Le Digabel & Nenad Mladenovi'{c}, 2004. "Pooling Problem: Alternate Formulations and Solution Methods," Management Science, INFORMS, vol. 50(6), pages 761-776, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:658-670. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.